MinT - Best Known (215−59, 215, s)-Nets in Base 3

Best Known (215−59, 215, s)-Nets in Base 3

(215−59, 215, 288)-Net over F₃ — Constructive and digital

Digital (156, 215, 288)-net over F₃, using

t-expansion [i] based on digital (155, 215, 288)-net over F₃, using
- 1 times m-reduction [i] based on digital (155, 216, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 72, 96)-net over F₂₇, using
    - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
        an explicitly constructive algebraic function field [i]

(215−59, 215, 637)-Net over F₃ — Digital

Digital (156, 215, 637)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(215−59, 215, 19332)-Net in Base 3 — Upper bound on s

There is no (156, 215, 19333)-net in base 3, because

1 times m-reduction [i] would yield (156, 214, 19333)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 272186 176588 616134 597912 139475 900882 670721 848670 464198 948811 705356 858792 784022 221342 732094 165223 942331 > 3²¹⁴ [i]